Sparse reconstruction with multiple Walsh matrices

References

[1] R. Baraniuk, V. Cevher, M. F. Duarte and C. Hegde, Model-based compressive sensing, IEEE Trans. Inform. Theory 56 (2010), no. 4, 1982–2001. 10.1109/TIT.2010.2040894Suche in Google Scholar

[2] R. Baraniuk, M. Davenport, R. DeVore and M. Wakin, A simple proof of the restricted isometry property for random matrices, Constr. Approx. 28 (2008), no. 3, 253–263. 10.1007/s00365-007-9003-xSuche in Google Scholar

[3] R. Basri and D. W. Jacobs, Lambertian reflection and linear subspaces, IEEE Trans. Pattern Anal. Mach. Intell. 25 (2003), no. 3, 218–233. 10.1109/TPAMI.2003.1177153Suche in Google Scholar

[4] P. Belhumeur, J. Hespanha and D. Kriegman, Eigenfaces versus Fisherfaces: Recognition using class specific linear projection, IEEE Trans. Pattern Anal. Mach. Intell. 19 (1997), no. 7, 711–720. 10.1109/34.598228Suche in Google Scholar

[5] T. Blumensath and M. Davies, Iterative hard thresholding for compressed sensing, Appl. Comput. Harmon. Anal. 27 (2009), no. 3, 265–74. 10.1016/j.acha.2009.04.002Suche in Google Scholar

[6] A. Bruckstein, D. L. Donoho and M. Elad, From sparse solutions of systems of equations to sparse modeling of signals and images, SIAM Rev. 51 (2009), no. 1, 34–81. 10.1137/060657704Suche in Google Scholar

[7] E. Candes, The restricted isometry property and its implications for compressed sensing, C. R. Math. Acad. Sci. Paris 346 (2008), no. 9–10, 589–592. 10.1016/j.crma.2008.03.014Suche in Google Scholar

[8] E. Candes, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory 52 (2006), no. 2, 489–509. 10.1109/TIT.2005.862083Suche in Google Scholar

[9] E. Candes, J. Romberg and T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math. 59 (2006), no. 8, 1207–1223. 10.1002/cpa.20124Suche in Google Scholar

[10] A. Cohen, W. Dahmen and R. DeVore, Compressed sensing and best k-term approximation, J. Amer. Math. Soc. 22 (2009), no. 1, 211–231. 10.1090/S0894-0347-08-00610-3Suche in Google Scholar

[11] D. L. Donoho, Compressed sensing, IEEE Trans. Inform. Theory 52 (2006), no. 4, 1289–1306. 10.1109/TIT.2006.871582Suche in Google Scholar

[12] D. L. Donoho and J. Tanner, Counting faces of randomly projected polytopes when the projection radically lowers dimension, J. Amer. Math. Soc. 22 (2009), no. 1, 1–53. 10.1090/S0894-0347-08-00600-0Suche in Google Scholar

[13] S. Foucart, Sparse recovery algorithms: sufficient conditions in terms of restricted isometry constants, Approximation Theory XIII: San Antonio 2010, Springer Proc. Math. 13, Springer, New York (2012), 65–77. 10.1007/978-1-4614-0772-0_5Suche in Google Scholar

[14] S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing, Appl. Numer. Harmon. Anal., Birkhäuser, New York, 2013. 10.1007/978-0-8176-4948-7Suche in Google Scholar

[15] J. Haupt, W. U. Bajwa, G. Raz, S. Wright and R. Nowak, Toeplitz-structured compressed sensing matrices, IEEE/SP 14th Workshop on Statistical Signal Processing – SSP ’07, IEEE Press, Piscataway (2007), 294–298. 10.1109/SSP.2007.4301266Suche in Google Scholar

[16] F. Krahmer and R. Ward, New and improved Johnson–Lindenstrauss embeddings via the restricted isometry property, SIAM J. Math. Anal. 43 (2011), no. 3, 1269–1281. 10.1137/100810447Suche in Google Scholar

[17] M. Ledoux and M. Talagrand, Probability in Banach Spaces. Isoperimetry and Processes, Ergeb. Math. Grenzgeb. (3) 23, Springer, Berlin, 1991. 10.1007/978-3-642-20212-4Suche in Google Scholar

[18] K. Li and S. Cong, State of the art and prospects of structured sensing matrices in compressed sensing, Front. Comput. Sci. 9 (2015), no. 5, 665–677. 10.1007/s11704-015-3326-8Suche in Google Scholar

[19] S. Mendelson, A. Pajor and N. Tomczak-Jaegermann, Uniform uncertainty principle for Bernoulli and Subgaussian ensembles, Constr. Approx. 28 (2008), no. 3, 277–289. 10.1007/s00365-007-9005-8Suche in Google Scholar

[20] H. Rauhut, Random sampling of sparse trigonometric polynomials, Appl. Comput. Harmon. Anal. 22 (2007), no. 1, 16–42. 10.1016/j.acha.2006.05.002Suche in Google Scholar

[21] H. Rauhut, Compressive sensing and structured random matrices, Theoretical Foundations and Numerical Methods for Sparse Recovery, Radon Ser. Comput. Appl. Math. 9, Walter de Gruyter, Berlin, (2010), 1–92. Suche in Google Scholar

[22] H. Rauhut and R. Ward, Sparse Legendre expansions via l1-minimization, J. Approx. Theory 164 (2012), no. 5, 517–533. 10.1016/j.jat.2012.01.008Suche in Google Scholar

[23] M. Rudelson and R. Vershynin, On sparse reconstruction from Fourier and Gaussian measurements, Comm. Pure Appl. Math. 61 (2008), no. 8, 1025–1045. 10.1002/cpa.20227Suche in Google Scholar

[24] M. Talagrand, Majorizing measures: The generic chaining, Ann. Probab. 24 (1996), no. 3, 1049–1103. 10.1214/aop/1065725175Suche in Google Scholar

[25] J. A. Tropp, Greed is good: Algorithmic results for sparse approximation, IEEE Trans. Inform. Theory 50 (2004), no. 10, 2231–2242. 10.1109/TIT.2004.834793Suche in Google Scholar

[26] J. A. Tropp, Just relax: Convex programming methods for identifying sparse signals in noise, IEEE Trans. Inform. Theory 52 (2006), no. 3, 1030–1051. 10.1109/TIT.2005.864420Suche in Google Scholar

[27] J. A. Tropp, J. N. Laska, M. F. Duarte, J. Romberg and R. Baraniuk, Beyond Nyquist: Efficient sampling of sparse bandlimited signals, IEEE Trans. Inform. Theory 56 (2010), no. 1, 540. 10.1109/TIT.2009.2034811Suche in Google Scholar

[28] J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry and Y. Ma, Robust face recognition via sparse representation, IEEE Trans. Pattern Anal. Mach. Intell. 31 (2009), no. 2, 210–227. 10.1109/TPAMI.2008.79Suche in Google Scholar PubMed